“That is the sole focus of the government,” Mr Perrottet told AAP.

“We need to get through this as well as we can. We’re going to lead the nation out of this pandemic here in NSW, and there’s so many things to do in that space.”

The state is rapidly approaching its next vaccination milestone, just three days into the reopening triggered on Monday after 70 per cent of eligible residents got both jabs.

Some 444 new local COVID-19 cases were diagnosed in the 24 hours to 8pm on Tuesday and another four deaths as the state rapidly approaches its next vaccination milestone.

Some 75.23 per cent of residents over 16 are fully vaccinated and 90.77 per cent have had at least one dose.

NSW could reach the 80 per cent fully vaccinated milestone by Sunday, setting the stage for the next phase in the state’s reopening next week.

“The success of our vaccination rate has been absolutely superb … When we hit 80 per cent, we’ve always said it will be the Monday following,” Perrottet said.

The government’s COVID-19 and economic recovery committee – formerly known as crisis cabinet – will discuss tweaking the reopening roadmap on Thursday.

Perrottet could announce changes to regional travel restrictions and other restrictions on Friday.

As things currently stand, the next phase of the roadmap paves the way for outdoor gatherings of up to 50 vaccinated people, 20 guests in a home, dancing at hospitality venues and drinking standing up at the pub.

Travel across NSW would be allowed, as would carpooling, weddings of any size if the venue is large enough, and community sport.

NSW recorded 360 new infections and five deaths on Tuesday. Some 766 virus patients are in hospital, of whom 155 are in intensive care.

Late on Tuesday, NSW Health issued an alert for anyone who was on Qantas flight QF509 from Brisbane to Sydney on Saturday to get tested and isolate after a passenger tested positive for coronavirus.